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Simplifying 0.5x4 + -3x3 + 4x2 = 0 Reorder the terms: 4x2 + -3x3 + 0.5x4 = 0 Solving 4x2 + -3x3 + 0.5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(4 + -3x + 0.5x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(4 + -3x + 0.5x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + 0.5x2 = 0 Solving 4 + -3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 8 + -6x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -6x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6x + x2 = 0 + -8 -6x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6x + x2 = -8 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -8 + 9 Reorder the terms: 9 + -6x + x2 = -8 + 9 Combine like terms: -8 + 9 = 1 9 + -6x + x2 = 1 Factor a perfect square on the left side: (x + -3)(x + -3) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + -3) equal to 1 and -1.Subproblem 1
x + -3 = 1 Simplifying x + -3 = 1 Reorder the terms: -3 + x = 1 Solving -3 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1 + 3 x = 1 + 3 Combine like terms: 1 + 3 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -3 = -1 Simplifying x + -3 = -1 Reorder the terms: -3 + x = -1 Solving -3 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1 + 3 x = -1 + 3 Combine like terms: -1 + 3 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 2}Solution
x = {0, 4, 2}
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